17 Jul If the food is allocated equally between the sailors, how much utility will the second sailor receive?
For this question only, X = 1109. There are X pounds of food on an island that must be allocated between 2 marooned sailors.
The utility function of the first sailor is given by: 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 = 1 2 √𝐹1 Where F1 is the quantity of food consumed by the first sailor.
For the second sailor, utility (as a function of food consumption) is given by: 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 = 1 3 √𝐹2
i) If the food is allocated equally between the sailors, how much utility will the second sailor receive? [1 mark]
ii) How should the food be allocated between the sailors to ensure that they are both equally satisfied? [2 marks]
iii) Suppose that the second sailor requires a utility level of at least 5 to remain alive. How much food should be allocated to the first sailor to maximize the sum of utilities while ensuring that the second sailor remains alive?
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